All Questions
Tagged with matrix-decomposition cholesky-decomposition
62
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Factorizing $AMA^T+N=WW^T$ efficiently.
This question is related to this question with a slightly more general setting. A good speedup on this could improve performances of a decision process in multi-objective optimization that I designed.
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- 6,076
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62
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Cholesky factorization of $A M A^T$ for $M$ PSD with known Cholesky factorization.
In the context of my research, I am trying to efficiently compute/store a PSD matrix and the cholesky factorization might help.
Let $M\in\mathbb R^{n\times n}$ and $A\in\mathbb R^{m\times n}$ be such ...
- 6,076
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113
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Equivalence of the LDL decomposition with an upper-triangular or lower-triangular matrix
I am aware that given a positive-definite matrix $A$ we can compute its LDL decomposition as:
$$ A = L D L^t $$
where $L$ is a lower unit triangular matrix and $D$ a diagonal matrix.
In this paper by (...
- 103
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33
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Pivoted Cholesky - triangulate the resut?
I have implemented pivoted Cholesky from http://www.dfg-spp1324.de/download/preprints/preprint076.pdf. My expectation was that I would be able to use the resulting triangular matrix to easily solve ...
- 105
2
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383
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Condition number change in Cholesky matrix decomposition [closed]
Give a symmetric positive definite matrix $A$ that has a LDLT decomposition $A = L D L^{\top}$, why is the condition number of $A$ not less than that of matrix $D$, i.e., $\mbox{cond} (A) \geqslant \...
- 71
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31
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If $A\succ B\succ 0$ for $A,B$, then is $\| Ax\|_2 \ge \| Bx\|_2$?
I'm trying to prove the following statement, which really feels like it should be correct.
If $A\succ B \succ 0$ for symmetric $A,B$, then show that $||Ax||_2 \ge || Bx||_2$ for vector $x$.
The ...
- 105
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47
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How to find the $LU$ representation of a non-symmetric matrix?
I have a $3\times4$ matrix $A$, and I have to find matrices $L$ and $U$, such, that $A=LU$. But the problem is that the matrix is not symmetric, and I get a lot of variables. Any methods to do this?
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64
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Cholesky decomposition of matrix product, $A=BB^T$, where $B\in \mathbb{R}^{n\times m}$ [duplicate]
Assume $A=BB^T$, where $B\in \mathbb{R}^{n\times m}$ and therefore $A\in \mathbb{R}^{n\times n}$. The product $A$ is always symmetric positive definite. I want to find the Cholesky factor $A=LL^T$, ...
- 21
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86
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LDU and principal minors of symmetric positive definite matrix
Suppose $A$ is an $n\times n$ symmetric positive definite matrix. We know that $A$'s leading principal minors $m_1,m_2,\dots,m_n$ are positive.
Now suppose that $A$ has LDU decomposition $A=LDU$, and ...
- 421
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48
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Create correlated random numbers with specified mean and standard deviation
I have two series of numbers that have certain correlation coefficient $\rho$.
How can I make a two series of random numbers that have correlation $\rho$, $\mu = 0$ and $\sigma = 1$?
I tried using ...
2
votes
1
answer
199
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Cholesky inverse
I have the Cholesky decomposition $LL^T$ of a symmetric positive definite matrix. I then compute a result in the form of $A=LXL^T$, where $A$ and $X$ are also symmetric positive definite matrices.
I ...
- 2,196
1
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401
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Cholesky decomposition of a strictly diagonaly dominant symmetric matrix
I am studying for a exam and I thought about practicing the Cholesky decomposition.
If a matrix $A = A^{T}$ , the main diagonal of $A$ has only positive elements and in every row the absolute value of ...
- 189
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476
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Cholesky decomposition for symmetric positive semi-definite matrices
On page 5 here: https://stanford.edu/class/ee363/lectures/lmi-s-proc.pdf
$A$ and $B$ are decomposed into $A^{1/2} A^{1/2}$ and same for $B$.
Is this from Cholesky decomposition? Can someone prove ...
- 729
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712
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Cholesky decomposition of large matrices
I am trying to obtain the Cholesky decomposition of a huge $150,000 \times 150,000$ sparse matrix with randomly distributed non-zero elements. I have only the entries for which the values are non-zero....
- 31
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55
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Triangular solver memory complexity
Does anybody know about the memory complexity of triangular solver?
PyTorch Documentation: https://pytorch.org/docs/stable/generated/torch.triangular_solve.html
More about Triangular solver: http://...
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